第17页

信息发布者：
解：原式​$=3\sqrt {3}-2\sqrt {3}$​
​$= \sqrt {3}$​
解：原式​$=2\sqrt {3}+2\sqrt {3}-3\sqrt {3}$​
​$= \sqrt {3}$​
解：原式​$=6\sqrt {2}-3\sqrt {2}+6\sqrt {2}$​
​$= 9\sqrt {2}$​
解：原式​$=(9\sqrt 2+\frac 15×5\sqrt 2-4×\frac {\sqrt 2}2)÷4\sqrt 2 $​
​$=8\sqrt 2÷4\sqrt 2$​
​$ =2$​
解：原式​$=3\sqrt {2}-\sqrt {2}+2\sqrt {2}$​
​$= 4\sqrt {2}$​
解：原式​$=\frac {\sqrt {2}}{5}-\sqrt {6}+1÷5\sqrt {2}$​
​$=\frac {\sqrt {2}}{5}-\sqrt {6}+\frac {\sqrt {2}}{10}$​
​$= \frac {3}{10}\sqrt {2}-\sqrt {6}$​
解：
$(2+\sqrt{3})(2-\sqrt{3})+(\sqrt{2}-\sqrt{3})^2$
$=2^2-(\sqrt{3})^2+(\sqrt{2})^2-2\sqrt{2}·\sqrt{3}+(\sqrt{3})^2$
$=4-3+2-2\sqrt{6}+3$
$=6-2\sqrt{6}$
解：
$\frac{3-\sqrt{12}}{\sqrt{3}}+(3+\sqrt{3})(3-\sqrt{3})$
$=\frac{3}{\sqrt{3}}-\frac{\sqrt{12}}{\sqrt{3}}+3^2-(\sqrt{3})^2$
$=\sqrt{3}-\sqrt{4}+9-3$
$=\sqrt{3}-2+6$
$=\sqrt{3}+4$
解：
$\vert -\sqrt{2}\vert +(\sqrt{2}-\frac{1}{2})^2-(\sqrt{2}+\frac{1}{2})^2$
$=\sqrt{2}+[(\sqrt{2}-\frac{1}{2})-(\sqrt{2}+\frac{1}{2})][(\sqrt{2}-\frac{1}{2})+(\sqrt{2}+\frac{1}{2})]$
$=\sqrt{2}+(-1)×2\sqrt{2}$
$=\sqrt{2}-2\sqrt{2}$
$=-\sqrt{2}$
解：
$(2\sqrt{5}+3\sqrt{2})^2-(2\sqrt{5}-3\sqrt{2})^2$
$=[(2\sqrt{5}+3\sqrt{2})-(2\sqrt{5}-3\sqrt{2})][(2\sqrt{5}+3\sqrt{2})+(2\sqrt{5}-3\sqrt{2})]$
$=(6\sqrt{2})×(4\sqrt{5})$
$=24\sqrt{10}$
解：
$(4+\sqrt{15})^{2025}×(4-\sqrt{15})^{2026}$
$=(4+\sqrt{15})^{2025}×(4-\sqrt{15})^{2025}×(4-\sqrt{15})$
$=[(4+\sqrt{15})(4-\sqrt{15})]^{2025}×(4-\sqrt{15})$
$=(16-15)^{2025}×(4-\sqrt{15})$
$=1^{2025}×(4-\sqrt{15})$
$=4-\sqrt{15}$
解：
$(1+\sqrt{2}+\sqrt{3})×(1+\sqrt{2}-\sqrt{3})$
$=[(1+\sqrt{2})+\sqrt{3}][(1+\sqrt{2})-\sqrt{3}]$
$=(1+\sqrt{2})^2-(\sqrt{3})^2$
$=1+2\sqrt{2}+2-3$
$=2\sqrt{2}$
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